DE 26 18 535 A1, for example, has disclosed a linear ball bearing having a guide carriage which is guided on a guide rail in a longitudinally displaceable manner and is mounted in rolling contact on longitudinal sides of the guide rail via balls. The balls are arranged on each longitudinal side in at least two parallel ball rows encircling in endless ball channels. All the balls are held in cage pieces. A total of four balls are held all round in a cage piece, to be precise two balls of the one row and two balls of the other row. In order to eliminate possible distortion forces, provision is made for the cage pieces to be of elastic design in the running direction or for them to be provided with elastic means. End surfaces, touching one another, of cage pieces adjacent to one another extend only over part of the width of the cage pieces in order to avoid deformations on lobes which enclose the balls. If these lobes are deformed under undesirable contact, jamming of the balls may occur. The fact that the end surfaces, touching one another, of the cage pieces, as viewed transversely to the running direction, extend only over a small part of the width of the cage piece encourages undesirable tilting of this cage piece. However, in these known linear ball bearings, tilting is prevented by virtue of the fact that two balls each of both ball rows, that is to say a total of four balls, are mounted in a common cage piece. A disadvantage with this known cage, however, is that, on account of the considerable extent of the cage piece which is required in the running direction, tight deflecting radii in the deflecting region of the linear ball bearing can only be overcome with difficulty.